Statistics Concepts: Observational Studies, Bias, and Inference

Statistics Concepts and Definitions

Ex. 1:

Observational study: No cause-effect; just associations. Five Number Summary = Min, Q1, Median, Q3, Max

Factors: Explanatory variable (x). Covariance: + or – relation but not strength

Block design: Individuals sharing the same characteristic are pooled.

SRS (Simple Random Sample); Stratified: Sample distinct groups separately then combine them. Sample survey: Cross-sectional; collect data of a population at one point in time.

Multistage: Using SRS within SRSs.

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Probability Rules and Statistical Estimation Methods

Probability Theory Fundamentals

Probability Definition

Probability measures the likelihood that an event will occur.

  • The probability of an event A is often denoted as P(A). It can be calculated as: P(A) = m / n
    • m = number of favorable outcomes for event A
    • n = total number of possible outcomes
  • P(A) represents the theoretical probability of event A.

Probability is a basic tool in the study and application of statistical methods. Medicine, for instance, often involves probabilistic reasoning.

Properties of

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Key Concepts in Statistics: Data Analysis and Probability

Key Concepts in Statistics

Data and Variables

Statistics: A branch of science that deals with collecting, organizing, analyzing, interpreting, summarizing, and presenting data.

Unit/Individual: An object on which we take a measurement or observation (e.g., people, places, things).

Population: The collection of all individuals or units under consideration.

Sample: A subset of the population from which we obtain data.

Variable: Any characteristic or property of an individual.

  • Quantitative Data: Numerical
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Understanding Key Statistical Concepts and Theorems

Law of Large Numbers

If you take samples of larger and larger size from any population, then the mean (x̄) of the sample tends to get closer and closer to μ (the population mean).

Sampling Distribution

The sampling distribution of the mean approaches a normal distribution as n (the sample size) increases.

Central Limit Theorem

The larger the sample size, the more normal the distribution will be.

Standard Error

The standard error is the standard deviation of the distribution of the sample means. T-distributions

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Understanding Probability, Distributions, and Statistical Analysis

Understanding Probability

The probability of a given event may be defined as the numerical value given to the likelihood of the occurrence of that event. It is a number lying between ‘0’ and ‘1’. ‘0’ denotes the event which cannot occur, and ‘1’ denotes the event which is certain to occur. For example, when we toss a coin, we can enumerate all the possible outcomes (head and tail), but we cannot say which one will happen.

Permutations

Permutation means arrangement of objects in a definite

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Epidemiology: Key Concepts and Measures

Proportion: Numerator is always a subset of the denominator; dimensionless (0 to 1 or 0% to 100%).

Rates: Describe changes in one quantity per unit of time. Unit = 1/time. Range (0-infinity).

Risk

Equation

Proportion | Dimensionless (can be expressed as a percent) | Appropriate for fixed populations with minimal losses to follow-up because we assume everyone was followed for a specific period.

  • New Cases: Numerator. New, non-existing cases. For diseases that can occur more than once, it is the first occurrence
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